We investigate the potential of shape information in assisting the computer-aided diagnosis of Alzheimer's disease and its prodromal stage of mild cognitive impairment. We employ BrainPrint to obtain an extensive characterization of the shape of brain structures. BrainPrint captures shape information of an ensemble of cortical and subcortical structures by solving the 2D and 3D Laplace-Beltrami operator on tri-angular and tetrahedral meshes. From the shape descriptor, we derive features for the classification by computing lateral shape differences and the projection on the principal component. Volume and thickness mea-surements from FreeSurfer complement the shape features in our model. We use the generalized linear model with a multinomial link function for the classification. Next to manual model selection, we employ the elastic-net regularizer and stepwise model selection with the Akaike information criterion. Training is performed on data provided by the Alzheimer's Dis-ease Neuroimaging Initiative (ADNI) and testing on the data provided by the challenge. The approach runs fully automatically.